Answer:
The correct option is B.
Step-by-step explanation:
The formula for amount after compound interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where P is principal, r is rate of interest, n is number of times interest compounded in a period, t is number of years.
It is given that Felix took out an unsubsidized student loan of $40,000 at a 3.6% APR, compounded monthly. The amount after 33 month is
[tex]A=40000(1+\frac{0.036}{12})^{33}=44156.1074[/tex]
The amount after 33 month is $44156.1074. So, the new principle amount is $44156.1074.
The monthly payment of $44156.1074 for 20 years is
[tex]m=\frac{P.V.(\fracr)}{1-(1+r)^{-n}}[/tex]
Where, P.V. is present value, r is rate of interest and n is number of times interest compounded.
[tex]m=\frac{44156.1074(\frac{0.036}{12})}{1-(1+\frac{0.036}{12})^{-20\times 12}}[/tex]
[tex]m=258.362447711[/tex]
[tex]m\approx 258.36[/tex]
Therefore the correct option is B.
